Question

In a diagram there is a picture which is 16cm x 8cm surrounded by a border of width 4 cm forming a bigger rectangle. Are the two rectangles similar?

Here is the image. The quality is really bad but i hope its understanable

Answer 1

Your picture is fine! And no, they aren't similar.

Explanation:

The two rectangles will be similar if the ratio of their length to width are the same.

Let the width and length of the smaller rectangle be `w_s` and `l_s` respectively, and let `w_b` and `l_b` be the width and length of the larger rectangle (w and l for width and length, s and b for small and large, naturally).

`w_s=8"cm"`
`l_s=16"cm"`

So the ratio is `l_s/w_s=16/8`
`=2`

`w_b=w_s+8`
If its a border of 4cm all the way around, then this will be 8cm overall.
`w_b=8+8`
`=16"cm"`

`l_b=l_s+8`
`l_b=16+8`
`=24"cm"`

`l_b/w_b=24/16`
`=3/2`

`3/2!=2` therefore the two rectangles are not similar.